Solving one-dimensional third order nonlinear KdV equation using MacCormack method coupled with compact finite difference scheme

In this article, we have investigated the performance of a well-known predictor-corrector MacCormack method coupled with compact finite difference scheme for solving third order nonlinear Korteweg-de Vries equation.The numerical scheme has second order accuracy in time and the order of accuracy in space is the same as that of the order of a compact finite difference scheme used for approximating the spatial derivatives present in the equation. This compact version of the classical MacCormack method has a very good performance in comparison with its classical counterpart and some other existing approaches for solving the nonlinear KdV equation.